Answer:
w = 9 cm
Step-by-step explanation:
The figure shows two similar right triangles. Similar triangles have proportional corresponding sides.
Write a proportion between triangles' legs:
[tex]\dfrac{12}{12+4}=\dfrac{w}{12}\\ \\ \\\dfrac{12}{16}=\dfrac{w}{12}[/tex]
Cross multiply:
[tex]16\cdot w=12\cdot 12\\ \\16w=144\\ \\w=\dfrac{144}{16}\\ \\w=9[/tex]
